For several years on various Android devices, including my Pixel 3, I've been able to have a setup where, while navigating, I can ask my phone to read text messages. At some point, whether through an update or settings change, things changed. I can get it to where it acts like it will play the messages, but there is just silence before it prompts me whether I want to reply, etc. Essentially it's acting like the text message is blank.
This was the case in a Pixel 3, and the problem persisted when transferring my data to a Pixel 5. A factory reset without transferring my data to the Pixel 5 let me hear the messages while navigating, so I suspect there is some setting or permission I have that is not letting this happen, but it's not clear to me what that would be.
If needed I can give the current setting for various permissions or settings, but I don't know what ones are needed.